Figure 1 shows a perfectly insulated cylinder containing 0.050 kg of liquid nitrogen at a temperature of 70 K - AQA - A-Level Physics - Question 1 - 2019 - Paper 2
Question 1
Figure 1 shows a perfectly insulated cylinder containing 0.050 kg of liquid nitrogen at a temperature of 70 K.
A heater transfers energy at a constant rate of 12 W t... show full transcript
Worked Solution & Example Answer:Figure 1 shows a perfectly insulated cylinder containing 0.050 kg of liquid nitrogen at a temperature of 70 K - AQA - A-Level Physics - Question 1 - 2019 - Paper 2
Step 1
Calculate the Specific Heat Capacity of Liquid Nitrogen
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Answer
To find the specific heat capacity (
h) of liquid nitrogen, we first calculate the total energy supplied to the nitrogen using the formula:
Q=Pimest
where:
P=12W (power)
t=890s (time)
Thus,
Q=12W×890s=10680J
Next, we use the specific latent heat of vaporization and the formula for specific heat capacity:
h = \frac{Q}{m \Delta T}$$
where:
- $m = 0.050 \, kg$ (mass of nitrogen)
- $\\Delta T = 77 \, K - 70 \, K = 7 \, K$
Substituting in the values:
h = \frac{10680 , J}{0.050 , kg \times 7 , K} = 30600 , J , kg^{-1} , K^{-1}$$
Step 2
The work done by the nitrogen in the cylinder when expanding due to a change of state is X.
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Answer
Given that the specific latent heat of vaporization of nitrogen is 2.0×105Jkg−1, the energy required (Y) to change the state from liquid to gas can be calculated as:
Y=m×L=0.050kg×2.0×105Jkg−1=10000J
Step 3
The energy required to change the state of the nitrogen from a liquid to a gas is Y.
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To find whether X (work done) is greater than Y (energy required for phase change), we note:
The total energy supplied is 10680 J.
The energy required to change the state is 10000 J.
Since the work done (X) is generally considered to be the remaining energy after the phase change, we compare:
